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%I #9 Sep 08 2022 08:45:53
%S 837,7896,32176,129888,521920,2092416,8379136,33535488,134179840,
%T 536795136,2147332096,8589631488,34359132160,137437741056,
%U 549753389056,2199018405888,8796083322880,35184352690176,140737449558016
%N a(n) = 6*a(n-1)-8*a(n-2) for n > 2; a(0)=837, a(1)=7896, a(2)=32176.
%C Related to Reverse and Add trajectory of 775 in base 2: a(n) = A077077(4*n+3)/6, i.e. one sixth of fourth quadrisection of A077077.
%H Vincenzo Librandi, <a href="/A177846/b177846.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F a(n) = 2*4^(n+5)-37*2^(n+2) for n > 0.
%F G.f.: (837+2874*x-8504*x^2) / ((1-2*x)*(1-4*x)).
%F G.f. for the sequence starting at a(1): 8*x*(987-1900*x) / ((1-2*x)*(1-4*x)).
%t CoefficientList[Series[(837 + 2874 x - 8504 x^2)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o (PARI) {m=19; v=concat([837, 7896, 32176], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]); v}
%o (Magma) [837] cat [2*4^(n+5)-37*2^(n+2): n in [1..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y Cf. A077077 (Reverse and Add trajectory of 775 in base 2), A177843, A177844, A177845.
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, May 14 2010
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